In our system, each fuzzy set membership function, denoted , is represented by a trapezoidal function with five parameters (a,b,c,d,e) corresponding to the weighted interval in the figure 2 (e represents the uncertainty). In the figure 2, which represents a fuzzy set A, implies that the element x does not characterize totally the fact represented by fuzzy set A, but with a degree of membership equals to 0.6 [8].

Moreover two characteristics of fuzzy sets are represented:

• the core of A defined by and
• the support of A defined by .

However, in our system and algorithms, we use derived characteristics based on a parametric definition such as and as shown in figure 2.